A proton (mass=1.67*10^-27 kg) moves with a velocity of 6.00*10^6 m/sec. Upon colliding with a stationary particle of unknown mass, the proton rebounds upon its own path with a velocity of 4.00*10^6 m/sec. The collision sends the unknown particle forward with a velocety of 2.00*10^6 m/sec. What is the mass of the unknown particle.
Do this with conservaton of momentum.
Mr. Jallah
To find the mass of the unknown particle, we can use the principle of conservation of momentum.
Conservation of momentum states that the total momentum before a collision is equal to the total momentum after the collision, as long as no external forces are acting on the system.
Let's assume the mass of the unknown particle is M kg.
Given:
Mass of the proton (m1) = 1.67 * 10^(-27) kg
Initial velocity of the proton (v1) = 6.00 * 10^6 m/s
Final velocity of the proton (v1') = -4.00 * 10^6 m/s (since it rebounds)
Final velocity of the unknown particle (v2') = 2.00 * 10^6 m/s
Now we can use the conservation of momentum equation:
(mass of proton * initial velocity of proton) + (mass of unknown particle * initial velocity of unknown particle)
= (mass of proton * final velocity of proton) + (mass of unknown particle * final velocity of unknown particle)
(m1 * v1) + (M * 0) = (m1 * v1') + (M * v2')
Since the unknown particle is initially at rest, its initial velocity (v2) is 0.
Now we can substitute the given values into the equation:
(1.67 * 10^(-27) kg * 6.00 * 10^6 m/s) = (1.67 * 10^(-27) kg * -4.00 * 10^6 m/s) + (M * 2.00 * 10^6 m/s)
After substituting the values, we can solve for M:
(1.67 * 10^(-27) kg * 6.00 * 10^6 m/s) = (1.67 * 10^(-27) kg * -4.00 * 10^6 m/s) + (M * 2.00 * 10^6 m/s)
1.67 * 10^(-27) kg * 6.00 * 10^6 m/s = 1.67 * 10^(-27) kg * -4.00 * 10^6 m/s + 2.00 * 10^6 m/s * M
Simplifying the equation:
10.02 * 10^(-21) = -6.68 * 10^(-21) + 2.00 * 10^6 M
16.70 * 10^(-21) = 2.00 * 10^6 M
M = (16.70 * 10^(-21)) / (2.00 * 10^6)
M = 8.35 * 10^(-15) kg
Therefore, the mass of the unknown particle is approximately 8.35 * 10^(-15) kg.